1. Field of the Invention
Embodiments of the invention are most generally related to the field of optical modulation and opto-electronic imaging. More particularly, embodiments of the invention are directed to novel apparatus and methods that effect phase and absolute value of the amplitude, hereinafter amplitude, control over an optical wavefront, and to applications directed to atmospheric sensing, optical metrology, astronomical and ophthalmic imaging, adaptive optics and interferometry.
2. Description of Related Art
In optical interferometry one often needs to generate a particular function form for the variation of amplitude over a given transverse plane starting, for example, from a uniform plane wave. As a specific instance in optical metrology, one generates the family of Zernike polynomials using modern optical interferometers with special masks incorporated. These specified wavefronts are used to test the accuracy of a particular optical surface being fabricated. In addition there are other instances when a distorted wavefront needs to be corrected so as to provide a plane wave output or a converging wave of specific radius of curvature for the equiphase of the propagating wave. For instance, when an optical signal travels from point A to point B, the quality of the received signal is less than that of the transmitted signal. This degradation is due to variation in the uniformity of the medium (index of refraction) that the light propagates through in going from point A to point B. Common examples include the light from a star that is distorted by atmospheric turbulence; poor vision due to defects in the optics of the eye; and, noisy communication caused by a non-uniform index of refraction over the signal path.
Viewed simply, a point source of light such as a star, for example, radiates spherical wavefronts of light in all directions. A wavefront is the locus of points having the same phase i.e., have the same path length from the source. To a distant viewer on earth, the wavefront of the light traveling along the viewer's line of sight is in the form of a flat, uniform plane of light; i.e., a plane wavefront. However, when the index of refraction of the propagation medium changes, the path lengths are no longer equal or normal to the propagating plane wavefront. Instead, the wavefront is distorted or aberrated. Thus the phase of the wavefront is no longer uniform over the spatial extent of the wavefront.
Wavefront sensors are now commonly used to measure higher-order aberrations of a wavefront propagated through an optical system. A Shack-Hartmann sensor is often the principal component of modern ophthalmic wavefront measuring devices. Several other types of wavefront sensors are also commercially popular. Once a distorted wavefront is measured and quantified, it may be desirable to compensate the wavefront; i.e., to bring it back to its non-aberrated state. Deformable mirrors, referred to as adaptive or active optics (AO) depending upon their application, are well known in the art. An adaptive optics imaging system, for example, is designed to correct for phase distortions in the optical wavefront in near real time to obtain improved image quality. Adaptive optical imaging originated as a tool for improving the performance of ground-based large telescopes for astronomical imaging through atmospheric turbulence. Another application is the correction of atmospheric turbulence over horizontal propagation paths. Adaptive imaging techniques have also been applied to wavefront control of large astronomical telescopes by using high power lasers and guide stars to generate perturbed wavefronts for correction of the astronomical image. Adaptive optics and wavefront control are also commonly used in laser fusion to correct for minute phase perturbations as the laser beam propagates through various lenses of the system. The typical components used in a present day adaptive system are listed in Table 1.
TABLE 1Wavefront SensorsWavefront CorrectorsShack-Hartmann SensorContinuous membrane mirrors with PZTCurvature sensorSegmented mirrors with PZTShearing interferometerBimorph MirrorsSmartt interferometerMEM micro-mirrorsPyramid sensorLiquid Crystal SLMsConventional designs for wavefront correctors include segmented mirror devices with each mirror segment having tip/tilt and piston controls, and continuous membrane (analog) devices with a number of actuators on their back side for deforming the mirror surface. Bimorph mirror technology uses two piezoelectric wafers bonded together with an array of electrodes. The outer surface of one of the mirror acts as a mirror. These devices are most suitably used with a curvature sensor configuration. More recent technologies used for phase screens, as they are sometimes called, include liquid crystal spatial light modulators (SLMs) and analog-type MEMS based micro-mirrors. Spatial light modulation is used, for example, in the fields of optical information processing, projection displays, video and graphics monitors, televisions, astronomy and electrophotographic printing. There, optical beams are deflected by mirror arrays where it is desired to be able to individually phase adjust the reflected light from each mirror. Often, the phase screen in an AO telescope is the single most troublesome component in the system. Typically, the phase screen is an LCD used in transmission mode with a voltage applied in an x-y coordinate system, pixel by pixel. It can also take the form of multiple PZT actuators used to push or deform a smooth mirror membrane into an aberration compensating surface shape.
Cost is an important factor in choosing an appropriate deformable mirror technology for a given application. Piezo-activated (PZT) deformable mirrors can cost over $1000 per actuator, thus a large mirror array can be extremely expensive. MEMS devices are typically manufactured using fabrication methods developed in the semiconductor industry. Comparatively, MEMS technology offers a low-cost attractive alternative. There are generally two types of micro-mirror arrays: (1) Devices with piston and tip/tilt controls for micro-mirrors; and (2) simple ON/OFF type binary micro-mirror arrays. The state-of-the-art devices of the first type have ˜1000 micro-mirrors each about 300 microns on a side, and each having an ˜2 micron piston stroke motion and ˜7 kHz frame rate. The ON/OFF type (i.e., digital binary MEMS) devices on the other hand have close to a million mirror elements, each being ˜17 micron on a side. Digital binary MEMS mirror technology has been developed over the last two decades. Arrays consisting of ˜106 mirrors that impart binary (1,0) amplitude modulation to the incident wavefront at ˜10 kHz frame rates are now available commercially at low cost. They have found widespread application, for example, in projection display systems. In recent years other applications of these arrays have evolved, e.g. in generation of (1,0) mask patterns in lithography, for implementing a moving aperture in a confocal microscope, for obtaining multiplexing Hadamard type mask patterns in spectroscopy applications, etc. The ability to provide only (1,0) type amplitude modulation has thus far been treated as a limitation that has prevented their use in adaptive systems for phase correction. A new way of wavefront phase coding is required that will permit the use of binary mirror arrays for wavefront phase modulation.
It is possible to generate selected wavefronts using deformable MEMS mirrors or LCD spatial light modulators. There are, however, certain disadvantages associated with their use. These devices typically cannot work over a broad range of wavelengths from the visible to long wavelength infra-red. As mentioned above, the cost for a 1000×1000 actuator assembly is prohibitive. MEMS devices currently used in adaptive optics setups do not offer as high resolution as may be desired for a particular application. The control of a large mirror array is complex and a large MEMS array can be susceptible to backlash errors. Half-toned characterization of phase front, as will be described below and used in conjunction with embodiments of the instant invention, would require high computational loading using the aforementioned deformable mirror devices.
In view of the challenges and disadvantages associated with wavefront phase control using deformable mirrors and/or LCD SLMs, the inventors have recognized that significant benefits may be realized by the various embodiments and aspects of the invention described in detail below and as defined in the appended claims. As mentioned above, a new way of wavefront phase coding is required that will permit the use of digital binary mirror arrays for wavefront phase modulation. The ability to generate an arbitrary wavefront using only binary (ON/OFF) micro-mirror arrays combined with digital half-toning methods and differential propagation distances has several advantages over deformable analog MEMS mirrors or LC spatial light modulators. The benefits and advantages include, but are not limited to, the ability to generate arbitrary wavefronts using only binary (ON/OFF) micro-mirror arrays combined with digital half-toning methods; broadband performance over the wavelength range from the visible to LWIR; an effective frame size of ˜200×200 to 300×300 pixels using digital half-toning algorithms over, e.g., 3×3 or 5×5 mirror blocks at a fraction of the cost for comparable MEMS performance; resolution that far exceeds analog MEMS device capability; simpler operation; less susceptibility to backlash errors; lower computational load, easy system calibration; all digital architecture; environmental robustness and stability, and others that will be recognized by persons skilled in the art.
As used herein, the term ‘analog’ refers to a continuous membrane mirror surface that may be deformed by a number of actuators coupled to the rear surface of the membrane, or, to a MEMS device where the individual mirrors can be stepped over multiple positions instead of simple binary 0,1. In contrast, a ‘digital’ binary MEMS mirror, as that term will be used in conjunction with various embodiments and aspects of the invention described herein, will refer to a MEMS mirror array in which each individual mirror segment can only be in an “ON” position (referred herein below as having a 1 value and oriented to retro-reflect incident light) or an “OFF” position (referred to herein below as having a 0 value and tilt-oriented to reflect incident light away from the intended optical path).
FIG. 1 shows what is known as an Argand diagram, which is used to illustrate the geometric representation of a complex number as simply a point in the complex plane. An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and the y-axis as the imaginary axis, where z=(abs)z eiθ. In the figure, the radius of dashed circle represents the complex modulus (abs)z of z and the angle θ represents its complex argument or what can be called the phase. The phase, θ, corresponds to the counterclockwise angle from the positive real axis, i.e., the value of θ such that x=(abs)z (cos θ) and y=(abs)z (sin θ). Since a wavefront may be described by Euler's equation ei θ(x,y)=cos θ+i sin θ, in conjunction with various embodiments of the invention described herein below, the notation of the Argand diagram may be useful to the reader in illustrating various aspects of the invention.
The advantages and benefits provided by the teachings disclosed herein and the embodiments of the invention disclosed and claimed will become more apparent to persons skilled in the art in view of the following description and drawings.